High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)
High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)
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DOI：
10.1016/j.jcp.2021.110760
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
J. King;S. Lind
中科院分区：
文献类型：
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作者：
J. King;S. Lind
无网格方法在模拟复杂几何形状的流动方面具有很大的潜力，其区域离散化的难度大大降低。然而，许多无网格方法仅限于低阶精度。为了与传统的基于网格的方法竞争，高阶精度是必不可少的。局部各向异性基函数法（LABFM）是King等人提出的一种无网格方法。（2020）[20]，这使得能够在无序节点离散化上构建高度精确的差分算子。在这里，我们介绍了一些发展LABFM，在基函数的建设，模板优化，稳定，可变分辨率和高阶边界条件。有了这些发展，直接数值模拟的Navier-Stokes方程是可能的，在极高的顺序（高达10阶的特征节点间距内部）。我们数值求解等温可压缩Navier-Stokes方程的一系列几何形状：周期性和通道流，流经一个圆柱体，多孔介质。与解析解，发表的数值结果（使用谱元法），和实验的极好的协议。在复杂的几何形状的直接数值模拟的方法的潜力证明了亚音速和跨音速流动通过非均匀多孔介质在孔隙雷诺数高达R e p= 968的模拟。
Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties of domain discretisation greatly reduced. However, many mesh-free methods are limited to low order accuracy. In order to compete with conventional mesh-based methods, high order accuracy is essential. The Local Anisotropic Basis Function Method (LABFM) is a mesh-free method introduced in King et al.(2020)[20], which enables the construction of highly accurate difference operators on disordered node discretisations. Here, we introduce a number of developments to LABFM, in the areas of basis function construction, stencil optimisation, stabilisation, variable resolution, and high order boundary conditions. With these developments, direct numerical simulations of the Navier Stokes equations are possible at extremely high order (up to 10th order in characteristic node spacing internally). We numerically solve the isothermal compressible Navier Stokes equations for a range of geometries: periodic and channel flows, flows past a cylinder, and porous media. Excellent agreement is seen with analytical solutions, published numerical results (using a spectral element method), and experiments. The potential of the method for direct numerical simulations in complex geometries is demonstrated with simulations of subsonic and transonic flows through an inhomogeneous porous media at pore Reynolds numbers up to R e p= 968.